Integral Representation and Explicit Formula at Rational Arguments for Apostol–Tangent Polynomials

Integral Representation and Explicit Formula at Rational Arguments for Apostol–Tangent Polynomials

The Fourier series expansion of Apostol–tangent polynomials is derived using the Cauchy residue theorem and a complex integral over a contour. This Fourier series and the Hurwitz–Lerch zeta function are utilized to obtain the explicit formula at rational arguments of these polynomials. Using the Lip...

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Bibliographic Details
Main Authors: Cristina B. Corcino, Roberto B. Corcino, Baby Ann A. Damgo, Joy Ann A. Cañete
Format: Article
Language:English
Published: MDPI AG 2021-12-01
Series:Symmetry
Subjects:
tangent polynomials
bernoulli polynomials
euler polynomials
genocchi polynomials
generating functions
Fourier series
Online Access:https://www.mdpi.com/2073-8994/14/1/35
Description
Summary:The Fourier series expansion of Apostol–tangent polynomials is derived using the Cauchy residue theorem and a complex integral over a contour. This Fourier series and the Hurwitz–Lerch zeta function are utilized to obtain the explicit formula at rational arguments of these polynomials. Using the Lipschitz summation formula, an integral representation of Apostol–tangent polynomials is also obtained.
ISSN:2073-8994

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